Comments for MEDB 5502, Week 03

Topics to be covered

• What you will learn
  • Principal components analysis
  • Applications of principal components
  • Factor analysis
  • To be determined
  • To be determined
  • To be determined
  • To be determined
  • To be determined

Philosophy behind principal components, 1 of 4

• Reduce complexity by modeling inter-relationships
• Inter-rleationships are linear
  • There is no dependent or outcome variable in principal components analysis

Philosophy behind principal components, 2 of 4

• First principal component
  • Linear combination that accounts most variation
  • This linear combination is the first eigenvector
  • The amount of variation accounted for is the first eigenvalue

Philosophy behind principal components, 3 of 4

• Need to resolve an ambiguity
  • \(3X_1+5X_2-4X_3+7X_4-1X_5\) versus \(6X_1+10X_2-8X_3+14X_4-2X_5\)
  • Solution: require sum of squared coefficients to equal 1
  • Note: \(3^2+5^2+(-4)^2+7^2+(-1)^2=100\)
  • Use \(\frac{3}{10}X_1+\frac{5}{10}X_2-\frac{4}{10}X_3+\frac{7}{10}X_4-\frac{1}{10}X_5\)

Philosophy behind principal components, 4 of 4

• Second principal component
  • Linear combination that accounts second most variation
  • Must be uncorrelated with first principal components
  • This linear combination is the second eigenvector
  • The amount of variation accounted for is the second eigenvalue
• Third principal component defined similarly

Health-related Quality of Life, 1 of 6

data_dictionary: Health-related Quality of Life of Persons Living with Tuberculosis.sav

source: |
  Tornu, Eric ; Quarcoopome, Louisa  (2022),  “Health-related Quality of Life of Persons Living with Tuberculosis”, Mendeley Data,  V2, doi: 10.17632/jg4xp7883w.2

description: |
  From the original source: This data is on a study which accessed the health-related quality of life of persons living with Tuberculosis.

Health-related Quality of Life, 2 of 6

Howwouldyourateyourqualityoflife_1:
  values:
    '1': Poor
    '2': Neither poor nor good
    '3': Good
    '4': Very Good

HowSatisareyouwithyourhealth_2:
  values:
    '1': Very dissatisfied
    '2': Dissatisfied
    '3': Neither satisfied nor satisfied
    '4': Satisfied
    '5': Very Satisfied

Physicalpainprevents_3:
  values:
    '1': An extreme amount
    '2': Very much
    '3': A moderate amount
    '4': A little
    '5': Not at all

Health-related Quality of Life, 3 of 6

Howmuchmedicaltreatment_4:
  values:
    '1': An extreme amount
    '2': Very much
    '3': A moderate amount
    '4': A little
    '5': Not at all

Howmuchdoyouenjoylife_5:
  values:
    '1': Not at all
    '2': A little
    '3': A moderate amount
    '4': Very much
    '5': Extremely

Towhatextentdoyoufeelyourlifetobemeaningful_6:
  values:
    '1': Not at all
    '2': A little
    '3': A moderate amount
    '4': Very much
    '5': Extremely

Health-related Quality of Life, 4 of 6

Howwellareyouabletoconcentrate_7:
  values:
    '1': Not at all
    '2': A little
    '3': A moderate amount
    '4': Very much
    '5': Extremely

Howsafedoyoufeelinyourdailylife_8:
  values:
    '1': Not at all
    '2': A little
    '3': A moderate amount
    '4': Very much
    '5': Extremely

Howhealthyisyourphysicalenvironment_9:
  values:
    '1': Not at all
    '2': A little
    '3': A moderate amount
    '4': Very much
    '5': Extremely

Health-related Quality of Life, 5 of 6

Doyouhaveenoughenergyforeverydaylife_10:
  values:
    '1': Not at all
    '2': A little
    '3': A moderate amount
    '4': Very much
    '5': Extremely

Areyouabletoacceptyourbodilyappearance_11:
  values:
    '1': Not at all
    '2': A little
    '3': A moderate amount
    '4': Very much
    '5': Extremely

Haveyouenoughmoneytomeetyourneeds_12:
  values:
    '1': Not at all
    '2': A little
    '3': A moderate amount
    '4': Very much
    '5': Extremely

Health-related Quality of Life, 6 of 6

AvailableInformation_13:
  values:
    '1': Not at all
    '2': A little
    '3': A moderate amount
    '4': Very much
    '5': Extremely

Opportunityforleisureactivities_14:
  values:
    '1': Not at all
    '2': A little
    '3': A moderate amount
    '4': Very much
    '5': Extremely

Howwellareyouabletogetaround_15:
  values:
    '1': Very poor
    '2': Poor
    '3': Neither poor nor good
    '4': Good
    '5': Very Good

Correlation matrix, 1 of 3

Correlation matrix, 2 of 3

Correlation matrix, 3 of 3

Communalities

Eigenvalues

Scree plot

Component matrix

Live demo, Principal components analysis

Break #1

• What you have learned
  • Principal components analysis
• What’s coming next
  • Applications of principal components

Applications

• Visualization
  • Reduce high dimensional visualization
  • Fewer graphs
• Regression analysis
  • Fewer independent variables (rule of 15)
  • Removes collinearity

Visualization using two principal components

R-squared using four principal components

R-squared using all 24 variables

Live demo, Applications of principal components

Break #2

• What you have learned
  • Applications of principal components
• What’s coming next
  • Factor analysis

Philosophy behind factor analysis

• Variance equals information
• Covariance equals shared information
• Modeling shared information creates latent variables

Live demo, Factor analysis

Break #3

• What you have learned
  • Factor analysis
• What’s coming next
  • To be determined

Slide 05-04

Live demo, To be determined

Break #4

• What you have learned
  • To be determined
• What’s coming next
  • To be determined

Slide 05-05

Live demo, To be determined

Break #5

• What you have learned
  • To be determined
• What’s coming next
  • To be determined

Slide 05-06

Live demo, To be determined

Break #6

• What you have learned
  • To be determined
• What’s coming next
  • To be determined

Slide 05-07

Live demo, To be determined

Break #7

• What you have learned
  • To be determined
• What’s coming next
  • To be determined

Slide 05-08

Live demo, To be determined

Summary

• What you have learned
  • Principal components analysis
  • Applications of principal components
  • Factor analysis
  • To be determined
  • To be determined
  • To be determined
  • To be determined
  • To be determined

Additional topics??